Question

E2 a, b , va rog urgent... Este vorba despre nr complexe !
Dau coroana !!

Answer 1

Vom amplifica numitorii cu conjugatele acelor numere complexe.

a)
[tex]\frac{2+i}{3+5i}+\frac{2-i}{3-5i}=\frac{(2+i)(3-5i)}{(3+5i)(2-5i)}+\frac{(2-i)(3+5i)}{(3-5i)(3+5i)}=\frac{(2+i)(3-5i)+(2-i)(3+5i)}{3^2+5^2}=\\\\ =\frac{6-7i+5+6+7i+5}{34}=\frac{22}{34}=\frac{11}{17} [/tex]

b)
$\frac{1+i\sqrt{3}}{1-i\sqrt{3}}+\frac{1-i\sqrt{3}}{1+i\sqrt{3}}=\frac{(1+i\sqrt{3})^2}{1+3}+\frac{(1-i\sqrt{3})^2}{1+3}=\frac{1+2i\sqrt{3}-3+1-2i\sqrt{3}-3}{4}=\frac{-4}{4}=-1$